Distributions In The Physical And Engineering Sciences Volume 2

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Distributions In The Physical And Engineering Sciences Volume 2

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Author : Alexander I. Saichev
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-09-05

Distributions In The Physical And Engineering Sciences Volume 2 written by Alexander I. Saichev and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-05 with Mathematics categories.

Distributions in the Physical and Engineering Sciences is a comprehensive exposition on analytic methods for solving science and engineering problems. It is written from the unifying viewpoint of distribution theory and enriched with many modern topics which are important for practitioners and researchers. The goal of the books is to give the reader, specialist and non-specialist, useable and modern mathematical tools in their research and analysis. Volume 2: Linear and Nonlinear Dynamics of Continuous Media continues the multivolume project which endeavors to show how the theory of distributions, also called the theory of generalized functions, can be used by graduate students and researchers in applied mathematics, physical sciences, and engineering. It contains an analysis of the three basic types of linear partial differential equations--elliptic, parabolic, and hyperbolic--as well as chapters on first-order nonlinear partial differential equations and conservation laws, and generalized solutions of first-order nonlinear PDEs. Nonlinear wave, growing interface, and Burger’s equations, KdV equations, and the equations of gas dynamics and porous media are also covered. The careful explanations, accessible writing style, many illustrations/examples and solutions also make it suitable for use as a self-study reference by anyone seeking greater understanding and proficiency in the problem solving methods presented. The book is ideal for a general scientific and engineering audience, yet it is mathematically precise. Features · Application oriented exposition of distributional (Dirac delta) methods in the theory of partial differential equations. Abstract formalism is keep to a minimum. · Careful and rich selection of examples and problems arising in real-life situations. Complete solutions to all exercises appear at the end of the book. · Clear explanations, motivations, and illustration of all necessary mathematical concepts.

Distributions In The Physical And Engineering Sciences

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Author : Alexander I. Saichev
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Distributions In The Physical And Engineering Sciences written by Alexander I. Saichev and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Distributions in the Physical and Engineering Sciences is a comprehensive exposition on analytic methods for solving science and engineering problems which is written from the unifying viewpoint of distribution theory and enriched with many modern topics which are important to practioners and researchers. The goal of the book is to give the reader, specialist and non-specialist useable and modern mathematical tools in their research and analysis. This new text is intended for graduate students and researchers in applied mathematics, physical sciences and engineering. The careful explanations, accessible writing style, and many illustrations/examples also make it suitable for use as a self-study reference by anyone seeking greater understanding and proficiency in the problem solving methods presented. The book is ideal for a general scientific and engineering audience, yet it is mathematically precise.

Distributions In The Physical And Engineering Sciences

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Author : Alexander I. Saichev
language : en
Publisher: Springer Science & Business Media
Release Date : 1996-11-01

Distributions In The Physical And Engineering Sciences written by Alexander I. Saichev and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-11-01 with Mathematics categories.

A comprehensive exposition on analytic methods for solving science and engineering problems, written from the unifying viewpoint of distribution theory and enriched with many modern topics which are important to practioners and researchers. The book is ideal for a general scientific and engineering audience, yet it is mathematically precise.

Statistical Distributions In Engineering

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Author : Karl V. Bury
language : en
Publisher: Cambridge University Press
Release Date : 1999-01-13

Statistical Distributions In Engineering written by Karl V. Bury and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-01-13 with Mathematics categories.

This 1999 book presents single-variable statistical distributions useful in solving practical problems in a wide range of engineering contexts.

Convergence And Summability Of Fourier Transforms And Hardy Spaces

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Author : Ferenc Weisz
language : en
Publisher: Birkhäuser
Release Date : 2017-12-27

Convergence And Summability Of Fourier Transforms And Hardy Spaces written by Ferenc Weisz and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-27 with Mathematics categories.

This book investigates the convergence and summability of both one-dimensional and multi-dimensional Fourier transforms, as well as the theory of Hardy spaces. To do so, it studies a general summability method known as theta-summation, which encompasses all the well-known summability methods, such as the Fejér, Riesz, Weierstrass, Abel, Picard, Bessel and Rogosinski summations. Following on the classic books by Bary (1964) and Zygmund (1968), this is the first book that considers strong summability introduced by current methodology. A further unique aspect is that the Lebesgue points are also studied in the theory of multi-dimensional summability. In addition to classical results, results from the past 20-30 years – normally only found in scattered research papers – are also gathered and discussed, offering readers a convenient “one-stop” source to support their work. As such, the book will be useful for researchers, graduate and postgraduate students alike.

Topics In Classical And Modern Analysis

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Author : Martha Abell
language : en
Publisher: Springer Nature
Release Date : 2019-10-21

Topics In Classical And Modern Analysis written by Martha Abell and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-21 with Mathematics categories.

Different aspects of harmonic analysis, complex analysis, sampling theory, approximation theory and related topics are covered in this volume. The topics included are Fourier analysis, Padè approximation, dynamical systems and difference operators, splines, Christoffel functions, best approximation, discrepancy theory and Jackson-type theorems of approximation. The articles of this collection were originated from the International Conference in Approximation Theory, held in Savannah, GA in 2017, and organized by the editors of this volume.

A First Course In Statistics For Signal Analysis

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Author : Wojbor A. Woyczynski
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-10-14

A First Course In Statistics For Signal Analysis written by Wojbor A. Woyczynski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-14 with Mathematics categories.

This self-contained and user-friendly textbook is designed for a first, one-semester course in statistical signal analysis for a broad audience of students in engineering and the physical sciences. The emphasis throughout is on fundamental concepts and relationships in the statistical theory of stationary random signals, which are explained in a concise, yet rigorous presentation. With abundant practice exercises and thorough explanations, A First Course in Statistics for Signal Analysis is an excellent tool for both teaching students and training laboratory scientists and engineers. Improvements in the second edition include considerably expanded sections, enhanced precision, and more illustrative figures.

The Xft Quadrature In Discrete Fourier Analysis

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Author : Rafael G. Campos
language : en
Publisher: Springer
Release Date : 2019-05-24

The Xft Quadrature In Discrete Fourier Analysis written by Rafael G. Campos and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-24 with Mathematics categories.

This book has two main objectives, the first of which is to extend the power of numerical Fourier analysis and to show by means of theoretical examples and numerous concrete applications that when computing discrete Fourier transforms of periodic and non periodic functions, the usual kernel matrix of the Fourier transform, the discrete Fourier transform (DFT), should be replaced by another kernel matrix, the eXtended Fourier transform (XFT), since the XFT matrix appears as a convergent quadrature of a more general transform, the fractional Fourier transform. In turn, the book’s second goal is to present the XFT matrix as a finite-dimensional transformation that links certain discrete operators in the same way that the corresponding continuous operators are related by the Fourier transform, and to show that the XFT matrix accordingly generates sequences of matrix operators that represent continuum operators, and which allow these operators to be studied from another perspective.

Numerical Fourier Analysis

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Author : Gerlind Plonka
language : en
Publisher: Springer Nature
Release Date : 2023-11-08

Numerical Fourier Analysis written by Gerlind Plonka and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-08 with Mathematics categories.

New technological innovations and advances in research in areas such as spectroscopy, computer tomography, signal processing, and data analysis require a deep understanding of function approximation using Fourier methods. To address this growing need, this monograph combines mathematical theory and numerical algorithms to offer a unified and self-contained presentation of Fourier analysis. The first four chapters of the text serve as an introduction to classical Fourier analysis in the univariate and multivariate cases, including the discrete Fourier transforms, providing the necessary background for all further chapters. Next, chapters explore the construction and analysis of corresponding fast algorithms in the one- and multidimensional cases. The well-known fast Fourier transforms (FFTs) are discussed, as well as recent results on the construction of the nonequispaced FFTs, high-dimensional FFTs on special lattices, and sparse FFTs. An additional chapter is devoted to discrete trigonometric transforms and Chebyshev expansions. The final two chapters consider various applications of numerical Fourier methods for improved function approximation, including Prony methods for the recovery of structured functions. This new edition has been revised and updated throughout, featuring new material on a new Fourier approach to the ANOVA decomposition of high-dimensional trigonometric polynomials; new research results on the approximation errors of the nonequispaced fast Fourier transform based on special window functions; and the recently developed ESPIRA algorithm for recovery of exponential sums, among others. Numerical Fourier Analysis will be of interest to graduate students and researchers in applied mathematics, physics, computer science, engineering, and other areas where Fourier methods play an important role in applications.

Functions Of Bounded Variation And Their Fourier Transforms

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Author : Elijah Liflyand
language : en
Publisher: Springer
Release Date : 2019-03-06

Functions Of Bounded Variation And Their Fourier Transforms written by Elijah Liflyand and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-06 with Mathematics categories.

Functions of bounded variation represent an important class of functions. Studying their Fourier transforms is a valuable means of revealing their analytic properties. Moreover, it brings to light new interrelations between these functions and the real Hardy space and, correspondingly, between the Fourier transform and the Hilbert transform. This book is divided into two major parts, the first of which addresses several aspects of the behavior of the Fourier transform of a function of bounded variation in dimension one. In turn, the second part examines the Fourier transforms of multivariate functions with bounded Hardy variation. The results obtained are subsequently applicable to problems in approximation theory, summability of the Fourier series and integrability of trigonometric series.